Question

Fill in the blanks below to make a true statement. In a binomial experiment with n trials and probability of success p, if np (1 - p) ≥ 10, the binomial random variable X is approximately normal with mu X= ___ and sigma X= _____
a. 10. 100.
b. np ( 1 - p ) . 5. np.
c. np/( 1 - p ).

Answer 1

Answer:

$\mu_{x}=np$

$\sigma^2_{X}=np(1-p)$

Step-by-step explanation:

∵ When x is a random variable having distribution B(n, p), then for sufficiently large value of n, the following random variable has a standard normal distribution,

$\frac{x-\mu}{\sigma}\sim N(0,1)$

Where,

$\mu=np$

$\sigma^2=np(1-p)$

Here the variable X has a binomial distribution,

Such that, np (1 - p) ≥ 10 ⇒ n is sufficiently large.

Where, n is the total numbers of trials, p is success in each trials,

So, the mean of variable X is,

$\mu_{X} = np$

And, variance of variable X is,

$\sigma^2{X}=np(1-p)$